Tracy Antonelli was 4 when she was diagnosed with thalassemia, a rare blood disorder that occurs often enough in Mediterranean countries like Italy that an old adage, uttered only partially in jest, warns Italian-Americans against marrying other Italian-Americans.

In 2002, Tracy wed Patrick Mooty, whose background is mostly Irish. Their three daughters — 7-year-old Emmilene, 6-year-old Rosalie and 3-year-old Francesca — all have thalassemia, but not through the accident of the couple’s genetics. Tracy and Patrick adopted the girls from China, specifically because they, too, have the potentially life-threatening disease, which, according to conservative estimates, occurs in about 10,000 pregnancies a year in China and about 600 a year in the United States.

“This is the most rewarding, perfect experience I’ve had in my life,” says Tracy. …